The topology of Stein fillable manifolds in high dimensions I

Jonathan Bowden, Diarmuid Crowley, Andras I. Stipsicz

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Abstract

We give a bordism-theoretic characterization of those closed almost contact (2q+1)-manifolds (with q≥2) that admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected almost contact 7-manifold with torsion-free second homotopy group is Stein fillable. We also discuss the Stein fillability of exotic spheres and examine subcritical Stein fillability.
Original languageEnglish
Pages (from-to)1363-1401
Number of pages40
JournalProceedings of the London Mathematical Society
Volume109
Issue number6
Early online date16 Jul 2014
DOIs
Publication statusPublished - Dec 2014

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Stein Manifold
Higher Dimensions
Exotic sphere
H-principle
Contact
Bordism
Topology
Contact Structure
Homotopy Groups
Torsion-free
Surgery
Closed

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The topology of Stein fillable manifolds in high dimensions I. / Bowden, Jonathan; Crowley, Diarmuid; Stipsicz, Andras I. .

In: Proceedings of the London Mathematical Society, Vol. 109, No. 6, 12.2014, p. 1363-1401.

Research output: Contribution to journalArticle

Bowden, Jonathan ; Crowley, Diarmuid ; Stipsicz, Andras I. . / The topology of Stein fillable manifolds in high dimensions I. In: Proceedings of the London Mathematical Society. 2014 ; Vol. 109, No. 6. pp. 1363-1401.
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